The unboundedness of Hausdorff operators on Quasi-Banach spaces
In this note, we show that the Hausdorff operator $H_Φ$ is unbounded on a large family of Quasi-Banach spaces, unless $H_Φ$ is a zero operator.
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arXiv subjects
Jianmiao Ruan
Publications and source records attributed to Jianmiao Ruan.
Some estimates for the bilinear fractional integrals on the Morrey space
In this paper, we are interested in the following bilinear fractional integral operator $B\mathcal{I}_α$ defined by \[ B\mathcal{I}_α({f,g})(x)=\int_{% %TCIMACRO{\U{211d} }% %BeginExpansion \mathbb{R} %EndExpansion ^{n}}\frac{f(x-y)g(x+y)}{|y|^{n-α}}dy, \] with $0< α<n$. We prove the weighted boundedness of $B\mathcal{I}_α$ on the Morrey type spaces. Moreover, an Olsen type inequality for $B\mathcal{I}_α$ is also given.
math.CA↗
Weighted Morrey estimates for Hausdorff operator and its commutator on the Heisenberg group
In this paper, we study the high-dimensional Hausdorff operators, defined via a general linear mapping $A$, and their commutators on the weighted Morrey spaces in the setting of the Heisenberg group. Particularly, under some assumption on the mapping $A$, we establish their sharp boundedness on the power weighted Morrey spaces.
math.CA↗